1. FIELD OF THE INVENTION
This invention relates to the field of image processing and image transformation.
2. BACKGROUND ART
In computer graphics applications, source images are created and manipulated by a user to achieve a variety of effects. A user may, among other operations, rotate, invert, animate, distort, resize, color or combine images. A computer graphics or imaging system provides a tool to accomplish these operations. One method of distorting an image is known as "warping."
The term warping is often used in image processing and computer graphics to mean a two-dimensional "resampling" of an image. In general, warping is a mapping of a two-dimensional planar region onto a two-dimensional surface. In certain computer graphic applications, an image may be mapped onto a two-dimensional projection of a three-dimensional surface or portion of a surface.
In many applications, distortions, abberations, or other flaws are introduced by sensors that are used to obtain data to generate a source image. These sensors can be any means for capturing or creating a source image, such as, for example, lenses, magnetic resonant imaging, cat scans, and digitized scans of existing images. It is highly desirable to be able to remove imperfections introduced by the sensors from the source image. Filtering is not always able to remove certain types of flaws. Thus, image warping is used.
In other instances, it may be desired to introduce distortions to an image for artistic or other reasons. In addition, by creating sequences of deformed images, each one slighly different than the one before, animated sequences can be produced by using warping.
An image warp, whether to remove or introduce distortion to a source image, is created and applied to the source image. The image warp may be a purely mathematical expression of varying degrees of complexity; (sphere, ellipsoid, etc). The image warp may also be a three-dimensional texture representation.
In image processing, warping functions are typically characterized or referred to by order of the warping function, i.e., an "nth order warp." For example, a "first order warp" is a linear function, an example of which is a "resize." A second order warp is a quadratic function, such as a "pin cushion" effect or "barrel" effect. A third order warp is described by a cubic polynomial function.
Warping functions can be wholly arbitrary functions. Thus, warping functions are not limited to closed-form mathematical descriptions (such as a hemisphere or other simple form), or to symmetrical forms. For example, a warping function can be described by a flexible surface which is pressed or stretched at many locations to form an arbitrary three-dimensional surface. This arbitrary surface is then applied to an existing image which is distorted to conform to the irregularities in a two dimensional projection of the arbitrary surface.